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**The Equations of Motion**

Kinematics The Equations of Motion

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Equations of Motion The equations of motion all apply to a body moving… …with constant acceleration …in a straight line. They can also be applied to projectile motion.

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**1. The average velocity equation:**

We know that if an object accelerates uniformly from an initial velocity (u) to a final velocity (v) over a time (t) then… If it has travelled through a displacement (s) then also… So… Or… Average velocity = u + v Average velocity = s t s = u + v t a s = ½ (u + v) t

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**2. The acceleration equation**

We know that acceleration is given by… Rearranging gives… Acceleration = v - u t v = u + at b

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**3. The displacement equation**

Substituting b into a gives… So… s = ½ (u + u + at) t s = ½ (2u + at) t c s = ut + ½ at2

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**The fourth equation t = 2s (u+v) (v–u) (u+v) = 2as v = u + a 2s (u+v)**

Rearranging a gives… Substituting into b gives… Rearranging… So… Expand the brackets… Simplifies to… t = s (u+v) (v–u) (u+v) = 2as v = u + a 2s (u+v) uv + v2 – u2 – uv = 2as v-u = 2as (u+v) v2 = u2 + 2as d

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Note: When recalling the equations of motion, check for homogeneity if you’re not sure. e.g. s = ut + ½ at2

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Question First watch this video. Now, analyse the video to determine… - fall time - height of cliff - velocity upon impact

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2.1 Position, Velocity, and Speed 2.1 Displacement x x f - x i 2.2 Average velocity 2.3 Average speed

2.1 Position, Velocity, and Speed 2.1 Displacement x x f - x i 2.2 Average velocity 2.3 Average speed

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